I am like Momof4 in that I allow parents to pay monthly or biweekly. I prefer monthly as it is less accounting, but that is hard for a lot of parents, so many of them are biweekly. The key I have found to this is that I get them all paying on the same day (so if someone starts their child with me on a non-pay week, I just get them to pay the first week and then it gets them onto the same schedule as everyone else). That way I always know when payday is and then with the monthly it is on the 1st, so pretty easy as well.
However, I would be concerned for sure with a parent trying to negotiate the holding fee/deposit. My contract and fees are not open to negotiation.